# Graphing Quadratics Using the TI-83

**Unit Objectives**

1. Students will be able to solve quadratic equations using the quadratic
formula.

2. Students will be able to identify and use the properties of quadratic
equations.

3. Students will be able to use quadratic equations to solve problems about
paths of

projectiles.

4. Students will be able to graph equations of the form y = ax^{2} + bx + c.

**New York State Standards: ( Math A )**

2A Understand and use rational and irrational numbers.

3A Use addition, subtraction, multiplication, division and exponentiation with
real

numbers and algebraic expressions .

7A Represent and analyze functions using verbal descriptions, tables, equations,
and

graphs.

7B Apply linear and quadratic functions in the solution of problems.

7C Translate among the verbal descriptions, tables, equations, and graphic forms
of

functions.

7D Model real -world situations with appropriate functions.

**NCTM Standards:**

• Numbers and Operations

• Algebra

• Communication

• Representations

**Materials and Equipment Needed**

• UCSMP Algebra Text

• Class Set of TI-83 Calculators

• Overhead with Calculator unit

• Computers with internet access

**Overview:
Day1:**

Students will be assigned group projects that will be one assessment. Students will use

TI-83 graphing calculators to explore variations of y = ax

^{2}.

**Day 2:**

Students will explore graphing y = ax

^{2}+ bx + c on the website Exploremath.com.

**Day 3:**

Students will work with partners on Lesson Master 9-3B, Graphing with an Automatic

Grapher. (TI-83)

**Day 4:**

Student will explore real-world examples of parabolas.

**Day 5:**

Students will solve quadratic equations both with Quadratic Formula and PolySmlt App

on the TI-83.

**Day 1
Lesson Plan:
Objectives:**

1. Students will be able to graph and interpret equations of the form y = ax

^{2}.

2. Students will be able to recognize axis of symmetry from a table of values and

from a graph.

3. Students will be able to solve equations of the form ax

^{2}= k.

**Standards:**

• NCTM Standards covered: Algebra, Representation

• NYS Standards covered: 3A, 7A, 7C

Materials:

• Graphing calculators

• Student worksheet and overhead transparency of worksheet

• Overhead with calculator unit

**Opening Activity:**

Students will be given a card with a number 1 – 7 on it when they enter the room. There

will be four of each card. These represent project numbers on pgs. 605 – 606. The

students will be given 10 minutes to meet with their group members to discuss the

project, which will be due the day after the unit test. This will be one of the assessments.

**Developmental Activity:**

Students will return to their seats and work with their partners to complete the worksheet,

Exploring y = ax

^{2}. Students will then be selected to present their solutions to the class

either at the board or on the overhead TI-83 unit.

**Ticket Out:**

Students will have the last 5 minutes of class to respond to the following question, also to

address any concerns they had with the lesson.

What are the two most important pieces of information that are determined by the a in the

equation y = ax

^{2}?

**Homework:**

Read pgs. 548 – 551, complete pgs. 551-553 # 5 – 9, 12, 13.

**Teacher’s Notes:
Solutions to Developmental Activity:
#1 and #2:**

**#3:** Answers will vary

**#4 and #5:**

**#6:** Answers will vary

**Ticket Out:**

Answers will be collected as the students exit the room. The information will be
used to

assess the students understanding of the lesson covered.

**Solutions to Homework:**

5b.

5c. A parabola which opens up whose axis of symmetry is x
= 0 and whose vertex is

(0,0).

6b.

6c. A parabola which opens down whose axis of symmetry is
x = 0 and whose vertex is

(0,0).

7. (0,0)

8. x = 0 | 12. 144 ft. |

9. up, down | 13. 100 ft. |

**Exploring y = ax**^{2
}

**Name: ____________________
Period: _____
Directions: **With your partner complete the following questions using your
graphing

calculator to create graphs.

1. Graph the following equations in the y = window and use zoom standard to view the

graphs.

2. Sketch the graphs on the grid below.

3. What happens to the graph of y = ax^{2} when the value of
a gets larger? gets smaller?

4. Graph the following equations in the y = window and use
zoom standard to view the

graphs.

5. Sketch the graphs in the grid below.

6. What happens to the graph of y = ax^{2} when a changes
positive to negative?

**Day 2
Lesson Plan:
Objectives:**

1. Students will be able to interpret the graphs of equations of the form y = ax

^{2}+ bx

+ c.

2. Students will be able to identify the vertex, axis of symmetry, y-intercept, and xintercept(

s) if they exist.

Standards:

• NCTM Standards covered: Algebra, Representation

• NYS Standards covered: 7A, 7C

Materials:

• Computers with internet access

• Worksheets for students

**Opening Activity:**

Students will enter computer lab, take their seats, and log in to the computers as

previously instructed . They will given a worksheet as they enter, it will have the website

they have to find.

**Developmental Activity:**

Students will use the website to answer the questions on the worksheet regarding the

graph of y = ax

^{2}+ bx + c.

**Ticket Out:**

Students will have the last 5 minutes of class to respond to the following question, also to

address any concerns they had with the lesson.

What happens to the graph of y = ax

^{2}+ bx + c when the value of c changes?

**Homework:**

Read pgs. 554 – 557, complete pgs. 558 – 559 #5, 7, 9, 12

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